When a lady has an orgasm, there is naturally moisture that can come out of her vagina. It will carry out whatever is inside.
You might be having the normal eggwhite cervical mucus at mid-cycle and then general discharge at other times, with possibly just a bit of a yeast infection going on that gives you the more chunky looking discharge. It could come out when you masturbate even if it isn't noticeable at other times.
Over-the-counter products are readily available to deal with yeast infections, at any pharmacy and even big grocery stores. To rule out a yeast infection, I would suggest using one. My co-Community Leader often recommends Monistat.
The link to masturbation also might be from the way you do it. For example, if you are wearing the underpants you wore all day and simply press hard on the outside in order to stimulate your clitoris, some bacteria or fungus could have gained entry. Or, if you use fingers inside your vagina, they might have picked something up. After you try the Monistat or other product, and if you think things are clear, you might limit masturbation to after a bath, when fingers and lady part are really clean.
Does the discharge itch? Yeast doesn't have to be white and chunky can be a matter of degree. Itching is almost always present though. Discharge after masturbation, an increase in, is normal. Your body is making additional lubrication and discharge accumulates. Let me know if it itches.